40% of the boys, 70% of the girls in a class attend a picnic and ratio of boys to girls in the class is 3:2 if the number on the picnic was 27. How many are there in the whole class?

1 Answer
KillerBunny
Jun 28, 2018

The total is approx. #52# students. It seems a little bit odd that the result is not an integer, given the nature of the problem, but I don't think I did anything wrong.

Explanation:

Let #b# be the number of boys and #g# be the number of girls. We know that #40%# of the boys and #70%# of the girls attended the picnic, and there were #27# students overall. This leads to the following equation:

#0.4b+0.7g = 27#

Moreover, we know that the ratio between boys and girls is #3/2#. This can be written as

#b/g=3/2#

which leads to

#b=3/2g#

substitute this expression in the one we wrote before to get

#0.4b+0.7g = 27 \iff 0.4(3/2g)+0.7g = 27#

you can reduce the equation to get

#1.3g=27#

and thus

#g = 27/1.3 \approx 20.8#

Plug this result in the boys-to-girl ratio to get

#b = 3/2g approx 3/2 * 20.8 = 31.2#

So, the total is #b+g approx 20.8 + 31.2 = 52#

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